Partial fourier codebooks associated with multiplied golay complementary sequences for compressed sensing

Authors:
Xiao Bian;Nam Yul Yu
Affiliations:
Department of Electrical Engineering, Lakehead University, Thunder Bay, Ontario, Canada;Department of Electrical Engineering, Lakehead University, Thunder Bay, Ontario, Canada
Venue:
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
Year:
2012

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Abstract

A new (N, K) partial Fourier codebook is constructed, associated with a binary sequence obtained by an element-wise multiplication of a pair of binary Golay complementary sequences. In the codebook, N=2m for a positive integer m, and K is approximately $\frac{N}{4}$. It is shown that the maximum magnitude of inner products between distinct code vectors is nontrivially bounded in the codebook, which is approximately up to $\sqrt{6}$ times the Welch bound equality for large N=2m with odd m. Finally, the new codebook is employed as a deterministic sensing matrix for compressed sensing, where its recovery performance is tested through numerical experiments.